IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2201-d846639.html
   My bibliography  Save this article

Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations

Author

Listed:
  • Anatoliy A. Pogorui

    (Department of Mathematics, Zhytomyr State University, Valyka Berdychivska St., 40, 10008 Zhytomyr, Ukraine)

  • Anatoliy Swishchuk

    (Department of Mathematics & Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada)

  • Ramón M. Rodríguez-Dagnino

    (School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, C.P., Monterrey 64849, Nuevo León, Mexico)

Abstract

In this paper, we study collisions of two telegraph particles on a line that are described by telegraph processes between collisions. We obtain an asymptotic estimation of the number of collisions under Kac’s condition for the cases where the direction-switching processes have the same parameters and different parameters. We also consider the application of these results to evaluate Margrabe’s spread option for two assets of spot prices modeled by two telegraph processes.

Suggested Citation

  • Anatoliy A. Pogorui & Anatoliy Swishchuk & Ramón M. Rodríguez-Dagnino, 2022. "Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2201-:d:846639
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2201/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2201/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jaehyuk Choi, 2018. "Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(6), pages 627-644, June.
    2. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    3. Anatoliy A. Pogorui & Anatoliy Swishchuk & Ramón M. Rodríguez-Dagnino, 2021. "Transformations of Telegraph Processes and Their Financial Applications," Risks, MDPI, vol. 9(8), pages 1-21, August.
    4. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matteo Gardini & Piergiacomo Sabino, 2022. "Exchange option pricing under variance gamma-like models," Papers 2207.00453, arXiv.org.
    2. Minqiang Li & Jieyun Zhou & Shi-Jie Deng, 2010. "Multi-asset spread option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 305-324.
    3. Juan Arismendi, 2014. "A Multi-Asset Option Approximation for General Stochastic Processes," ICMA Centre Discussion Papers in Finance icma-dp2014-03, Henley Business School, University of Reading.
    4. Pellegrino, Tommaso & Sabino, Piergiacomo, 2014. "On the use of the moment-matching technique for pricing and hedging multi-asset spread options," Energy Economics, Elsevier, vol. 45(C), pages 172-185.
    5. Leccadito, Arturo & Paletta, Tommaso & Tunaru, Radu, 2016. "Pricing and hedging basket options with exact moment matching," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 59-69.
    6. Jaehyuk Choi, 2018. "Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(6), pages 627-644, June.
    7. Ping Wu & Robert J. Elliott, 2017. "Valuation of certain CMS spreads," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(4), pages 445-467, November.
    8. Michael Samet & Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Ra'ul Tempone, 2022. "Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in L\'evy Models," Papers 2203.08196, arXiv.org, revised Oct 2023.
    9. Nicola Cufaro Petroni & Piergiacomo Sabino, 2015. "Cointegrating Jumps: an Application to Energy Facilities," Papers 1509.01144, arXiv.org, revised Jul 2016.
    10. Chun-Sing Lau & Chi-Fai Lo, 2014. "The pricing of basket-spread options," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1971-1982, November.
    11. Elisa Alòs & Jorge A. León, 2013. "On the closed-form approximation of short-time random strike options," Economics Working Papers 1347, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Kwangil Bae, 2019. "Valuation and applications of compound basket options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 704-720, June.
    13. Alexander Kushpel, 2015. "Pricing of high-dimensional options," Papers 1510.07221, arXiv.org.
    14. Alexander Kushpel, 2014. "Pricing of basket options I," Papers 1401.1856, arXiv.org.
    15. Kirkby, J. Lars & Nguyen, Dang H. & Nguyen, Duy, 2020. "A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    16. Roza Galeeva & Zi Wang, 2024. "Sector Formula for Approximation of Spread Option Value & Greeks and Its Applications," Commodities, MDPI, vol. 3(3), pages 1-33, July.
    17. Nagy, Tamás, 2013. "A villamos erőművek szén-dioxid-kibocsátásának modellezése reálopciók segítségével [Modelling of the carbon dioxide emissions of a power plant, using real options]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(3), pages 318-341.
    18. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    19. Hainaut, Donatien, 2022. "Pricing of spread and exchange options in a rough jump-diffusion market," LIDAM Discussion Papers ISBA 2022012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Pablo Olivares & Matthew Cane, 2014. "Pricing Spread Options under Stochastic Correlation and Jump-Diffusion Models," Papers 1409.1175, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2201-:d:846639. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.